Elastic buckling analysis of polygonal thin sheets under compression

In this work, we have studied elastic buckling of regular hexagonal thin sheets made of homogeneous and isotropic materials under in-plane hydrostatic and uniaxial compression, with internal supports, translational and rotational elastic edge supports, and a combination of free, simple-support and clamped boundary conditions. An energy method called Rayleigh-Ritz was utilized and the kinematic hypotheses of the classical thin plate buckling theory were applied. Displacement conditions were applied to edges and internal supports by employing proper basic P-Ritz functions. This approach gives an approximate analytical response that was calculated with Maple software and validated by previous researches. Moreover, the results were compared to numerical results obtained from ANSYS software. The findings revealed that besides having the advantages of other analytical methods, the Rayleigh-Ritz method is easy to use and straightforward to apply different constraints on boundaries and internal points; however, increasing the number of edges and constraints adds significantly the burden of calculation.